Explicitly covariant form of the integral Maxwell equations

J. L. Jiménez, G. Monsivais

Abstract


It is analyzed in detail the covariance of the integral forms of the Maxwell Equations. Different forms of writing the integral Maxwell equations in explicitly covariant form are analyzed. First we show how one of these ways can be obtained from the differential Maxwell equations, both from their usual three vector form as from their covariant four vector form. Then we discuss how this covariant integral Maxwell equations can be obtained from usual integral Maxwell equations. It is emphasized the necessity to write the usual integral equations without time derivatives. The integrations regions in the three-dimensional space and time are identified with parts of the same hyper-surface in four-dimensional space-time. This point is carefully analyzed.  Later we discuss other forms of the integral Maxwell equations. We show how these new versions can be expressed in an explicitly covariant form.

 


Keywords


Maxwell integral equations in explicitly covariant form, Covariant Maxwell integral equations, Classical integral electrodynamics in covariant form.

Full Text:

PDF

References


M. Bunge, Foundations of Physics(Springer, Berlin, 1969).

U. D. Barger and M. Olsson, Classical Electricity and Magnetism (Allyn and Bacon, Newton, Massachusetts, 1987).

D. Griffiths, Introduction to Electrodynamics, 3rd. ed. (Prentice Hall, En- Glenwood. Cliffs. NJ, 1999).

M. A. Heald and J.B. Marion, Classical Electromagnetic Radiation, 3rd ed. (Saunders C.P., Orlando, Florida, 1995).

H. Ohanian, Classical Electrodynamics, (Allyn and Bacon, Newton, Massachusetts, 1988).

M. Schwartz, Principles of Electrodynamics (McGraw Hill, New York, 1972).

J.D. Jackson, Classical Electrodynamics, 3rded. (Wiley, New York, 1999).

J. Vanderline, Classical Electromagnetic Theory, 2nd ed. (Kluwer A.P., Dordrecht, 2004).

B. DiBartolo, Classical Theory of Electromagnetism 2nd ed. (World Scientific, Singapore, 2004).

F.E. Low, Classical Field Theory. Electromagnetism and Gravitation, (Wiley, New York, 1997).

D.F. Lawden, Tensor Calculus and Relativity, (Methuen, London, 1967).

W. Pauli, Theory of Relativity, (Dover, New York, 1981).

C. Moller, The Theory of Relativity, 2nd ed. (Oxford U.P., Delhi, 1994).

J. L. Anderson, Principles of Relativity Physics, (Academic Press, New York, 1967).

J. Aharoni, The Special Theory of Relativity, 2nd ed. (Oxford U.P., London, 1965).

E. Ley Koo Rev. Mex. Fís. E 52, 84-89 (2006)

A. Kovetz, The Principles of Electromagnetic Theory, (Cambridge U.P., London, 1990).

Perhaps the most familiar form of the divergence theorem is

where is an arbitrary volume, the closed surface that surrounds it, and a vector valued function. If, for example, this theorem is applied to the function one obtains where is the projection of on the plane When this surface integral is evaluated using the parameters the projection is equal to (see Ref. [19]).

G. Monsivais and S. de Neymet, Teoremas de Green, Gauss y Stokes para funciones continuas y discontinuas, 2nd ed. (La Prensa de Ciencias, Facultad de Ciencias, UNAM, 2013).

D.V. Dazing, Proc. Camb. Phil. Soc. 30, 421-427 (1934).




DOI: https://doi.org/10.31349/RevMexFisE.18.76

Refbacks

  • There are currently no refbacks.


Revista Mexicana de Física E

ISSN: 2683-2216 (on line), 1870-3542 (print)

Semiannual publication of Sociedad Mexicana de Física, A.C.
Departamento de Física, 2o. Piso, Facultad de Ciencias, UNAM.
Circuito Exterior s/n, Ciudad Universitaria. C. P. 04510 Ciudad de México.
Apartado Postal 70-348, Coyoacán, 04511 Ciudad de México.
Tel/Fax: (52) 55-5622-4946, (52) 55-5622-4840. rmf@ciencias.unam.mx